Shutter speed – This is how quickly the cameras shutter plate opens and closes when taking the photo.
No matter what f stop you choose, (ie what size hole you want to let light in) the shutter plate itself must still open and close completely, to take the photo. It can do this either extremely quickly or extremely slowly taking several seconds. This speed chosen will impact the picture.
The measurement of shutter speed is given as a fraction of a second or greater than 1 second.
eg: 1/1000 means a thousandth of a second and ¼ means a quarter of a second and 4” means 4 seconds
Above is a simple diagram that explains this variant. As you can see the greater the shutter speed the sharper the clarity of the photo for a moving object. But remember this too, when you're dealing with landscapes, some objects are fixed, like rocks, stones, tree trunks, other objects move like leaves, branches, grass, water etc.
However, you have to remember that a fast shutter speed allows less time for the light to enter the camera. And this is the compromise.
Another factor to consider is the lens you are using. Focal length can affect the desired shutter speed you should use. Imagine looking at a subject with your own eyes. A tree in front of you. It is still, you can see what’s around it, behind it, in front of it. Your scene is wide and your subject is still (for the most part) Now imagine you are looking at that same tree through a foot long piece of pipe. Suddenly your subject is only a fraction of what you were seeing. You see a small round view focused on the trunk of the tree. The detail is clear because you are only focusing on the trunk but the trunk is wobbling slightly. Your pipe is wobbling up and down only slightly as you try to hold it perfectly still with your hands. As a result your tree trunk appears to move around even with the smallest of movements. This is the same principle when using long telephoto lens, and as a result you have to allow for this added movement in the frame.
The rule of thumb when taking pictures WITHOUT a tripod is – don’t choose a shutter speed greater than your focal length UNLESS you are using a tripod. Eg: if your lens is at 100mm prime, then don’t choose a shutter speed slower than 1/100. When taking landscapes more often than not, you are using a wide angle lens of some description anywhere from 50mm to 10mm, so generally you're pretty safe, going as slow as 1/100 of a second without a tripod. I know plenty of photographers who successfully shoot handheld at 1/50 but personally my limit is between 1/100 and 1/60, anything slower and it's not even worth taking the shot as the results are rubbish. But we're all different. There are no hard fixed rules, make your own mark and experiment. Don't get wrapped up in the rules of photography. Remember beauty is in the eye of the beholder.